I managed to set up my 2nd gen chromebook with cloudprint, which was pretty straight forward:

http://www.google.com/cloudprint/learn/

Use Google cloudprint. If you sign-in, it should list all the printers that are connected to any of your other computers where you're signed into Chrome (i.e. through Chrome settings, not just signed into gmail).

So I have to buy another computer just to send a file from my new computer to a printer?